Single-pulse two-qubit gates for Rydberg atoms with noncyclic geometric control

Arrays of neutral atoms have emerged as promising platforms for quantum computing. The realization of high-fidelity two-qubit gates with robustness is currently a significantly important task for large-scale operations. In this paper, we present a convenient approach for implementing a two-qubit controlled-phase gate with Rydberg blockade. We achieve noncyclic and geometric control within a single modulated pulse. Compared with the control scheme by cyclic evolution determined by dynamical parameters, the robustness of our proposal against systematic errors will be remarkably improved due to its geometric characteristics. Importantly, the noncyclic geometric control reduces the gate time for small rotation angles and is more insensitive to decoherence effects. Furthermore, we accelerate the adiabatic control with the aid of shortcuts to adiabaticity to further shorten the operation time. We apply our protocol to the quantum Fourier transformation algorithm to demonstrate the actual acceleration. Therefore, the proposed scheme provides analytical wave forms for arbitrary two-qubit gates and may play an important role in experiments involving atomic arrays.